Dipoles in graphene have infinitely many bound states

DOI10.1063/1.4904310zbMath1311.82055arXiv1403.7160OpenAlexW2061935292MaRDI QIDQ2939225

Heinz Siedentop, Jean-Claude Cuenin

Publication date: 19 January 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.7160

zbMATH Keywords

Mathieu equationDirac operatorKAM theoryMathieu functionspectral analysisone-dimensional Schrödinger operatorBessel equationnanostructuresnanoparticlesHill equationspheroidal wave functionnearly integrable Hamiltonian systemsselfadjoint operator theory in quantum theoryoperator cosine functionsLamé functionabstract operator algebras on Hilbert spacesclosed and approximate solutions to the Dirac equationclosed and approximate solutions to the Klein-Gordon equationclosed and approximate solutions to the Schrödinger equationhigher-order Cauchy problemsoperator sine function

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Abstract operator algebras on Hilbert spaces (47L30) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30) Operator sine and cosine functions and higher-order Cauchy problems (47D09) Lamé, Mathieu, and spheroidal wave functions (33E10) Nearly integrable Hamiltonian systems, KAM theory (70H08) Statistical mechanics of nanostructures and nanoparticles (82D80)

Related Items (9)

Dirac–Coulomb operators with infinite mass boundary conditions in sectors ⋮ Decoupling of deficiency indices and applications to Schrödinger-type operators with possibly strongly singular potentials ⋮ Schrödinger equation for non-pure dipole potential in 2D systems ⋮ Continuum limit for lattice Schrödinger operators ⋮ Eigenvalues of one-dimensional non-self-adjoint Dirac operators and applications ⋮ Accumulation rate of bound states of dipoles generated by point charges in strained graphene ⋮ Inverse scattering for Schrödinger operators on perturbed lattices ⋮ Accumulation rate of bound states of dipoles in graphene ⋮ Domains for Dirac-Coulomb min-max levels

Cites Work

• Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices
• Holomorphic families of Dirac operators
• Self-adjointness and invariance of the essential spectrum for Dirac operators defined as quadratic forms
• Spectral theory of the operator \((p^2+m^2)^{1/2}-Ze^2/r\)
• Wave operators and similarity for some non-selfadjoint operators
• Critical dipoles in one, two, and three dimensions
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